Consider the following dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25. What is the third quartile’s value? Round to the nearest tenth if necessary.(1 point)
To find the third quartile's value, we need to arrange the dataset in ascending order: 18, 20, 22, 22, 24, 25, 29, 30, 31.
Since we have 9 data points, the third quartile corresponds to the data point at position (9 + 1) * 3/4 = 7.5, which is between the 7th and 8th data points.
The 7th data point is 29 and the 8th data point is 30. To find the average of these two values, we add them together and divide by 2: (29 + 30) / 2 = 59 / 2 = 29.5.
Therefore, the third quartile's value is 29.5.
Given the following dataset, what are the extremes?
58, 32, 8, 25, 13, 12, 3, 11, 22, 10(1 point)
The smallest extreme value is
.
The largest extreme value is
.
To find the extremes in the dataset, we need to identify the smallest and largest values.
The smallest value in the dataset is 3 (as it is the lowest value).
The largest value in the dataset is 58 (as it is the highest value).
Therefore, the smallest extreme value is 3 and the largest extreme value is 58.
To find the third quartile's value, we first need to arrange the dataset in ascending order: 18, 20, 22, 22, 24, 25, 29, 30, 31.
The third quartile, also known as the upper quartile, divides the dataset into two halves. This means that 75% of the data is below the third quartile, and 25% is above.
Since we have 9 data points, the position of the third quartile can be calculated as follows:
Position = (75/100) * (Total number of data points + 1)
= (75/100) * (9 + 1)
= (75/100) * 10
= 7.5
Since we cannot have a decimal position, we take the average of the values at positions 7 and 8:
Third quartile's value = (Value at position 7 + Value at position 8) / 2
= (29 + 30) / 2
= 59 / 2
= 29.5
Therefore, the third quartile's value is 29.5.